There is a substantial collection of robust analysis of covariance (ANCOVA) methods that effectively deals with non-normality, unequal population slope parameters, outliers, and heteroscedasticity. Some are based on the usual linear model and others are based on smoothers (nonparametric regression estimators). However, extant results are limited to one or two covariates. A minor goal here is to extend a recently-proposed method, based on the usual linear model, to situations where there are up to six covariates. The usual linear model might provide a poor approximation of the true regression surface. The main goal is to suggest a method, based on a robust smoother, for dealing with curvature when there are three or four covariates. The results include perspectives on the curse of dimensionality. Perspectives on the use of a linear model versus a smoother are given.
Wilcox, R. (2018). Robust ANCOVA, curvature, and the curse of dimensionality. Journal of Modern Applied Statistical Methods, 17(2), eP2682. doi: 10.22237/jmasm/1551906370